Lab Report

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• Starter files
• main.tex2.9 KB

  \documentclass[11pt]{article}
  
  \usepackage[margin=1in]{geometry}
  \usepackage{amsmath}
  \usepackage{booktabs}
  \usepackage{siunitx}
  \usepackage{pgfplots}
  \pgfplotsset{compat=1.18}
  
  \title{Measuring the Acceleration Due to Gravity with a Simple Pendulum}
  \author{Your Name \\ Partner: Partner Name \\ PHYS 101, Section 2}
  \date{\today}
  
  \begin{document}
  
  \maketitle
  
  \begin{abstract}
  \noindent We measured the period of a simple pendulum at five lengths and
  extracted the local gravitational acceleration from the slope of $T^2$
  against $L$. We obtain $g = \SI{9.79 \pm 0.06}{\meter\per\second\squared}$,
  consistent with the accepted value. Replace this abstract with a
  three-sentence summary of aim, method, and result.
  \end{abstract}
  
  \section{Introduction}
  
  For small oscillations, the period of a simple pendulum of length $L$ is
  \begin{equation}
    T = 2\pi \sqrt{\frac{L}{g}},
    \qquad\text{so}\qquad
    T^2 = \frac{4\pi^2}{g} \, L,
    \label{eq:period}
  \end{equation}
  and $g$ follows from the slope of a linear fit of $T^2$ versus $L$.
  
  \section{Method}
  
  A steel bob on a light string was released from an angle below
  \ang{10}. For each length we timed \num{20} oscillations with a
  stopwatch (resolution \SI{0.01}{\second}) and repeated the measurement
  three times. Lengths were measured to the bob's center with a tape
  measure (\SI{1}{\milli\meter} resolution).
  
  \section{Results}
  
  \begin{table}[ht]
    \centering
    \begin{tabular}{S[table-format=1.3] S[table-format=1.3] S[table-format=1.3]}
      \toprule
      {$L$ (\si{\meter})} & {$T$ (\si{\second})} & {$T^2$ (\si{\second\squared})} \\
      \midrule
      0.200 & 0.899 & 0.808 \\
      0.400 & 1.271 & 1.615 \\
      0.600 & 1.556 & 2.421 \\
      0.800 & 1.797 & 3.229 \\
      1.000 & 2.009 & 4.036 \\
      \bottomrule
    \end{tabular}
    \caption{Mean period at each pendulum length.}
    \label{tab:data}
  \end{table}
  
  \begin{figure}[ht]
    \centering
    \begin{tikzpicture}
      \begin{axis}[
          width=0.7\linewidth, height=5.5cm,
          xlabel={$L$ (\si{\meter})}, ylabel={$T^2$ (\si{\second\squared})},
          xmin=0, ymin=0, grid=major]
        \addplot[only marks, mark=*] coordinates
          {(0.200,0.808) (0.400,1.615) (0.600,2.421) (0.800,3.229) (1.000,4.036)};
        \addplot[domain=0:1.05, samples=2, thick] {4.034*x};
      \end{axis}
    \end{tikzpicture}
    \caption{$T^2$ versus $L$ with linear fit; the slope gives
      $g = 4\pi^2/\text{slope}$.}
    \label{fig:fit}
  \end{figure}
  
  The fitted slope is \SI{4.034 \pm 0.024}{\second\squared\per\meter},
  giving $g = \SI{9.79 \pm 0.06}{\meter\per\second\squared}$.
  
  \section{Discussion}
  
  The result agrees with the accepted
  \SI{9.81}{\meter\per\second\squared} within one standard error. The
  dominant uncertainty is reaction time on the stopwatch; a photogate
  would reduce it. To adapt this report, replace the sections above with
  your experiment, or ask the agent in the chat alongside this document to
  draft or typeset it for you.
  
  \end{document}
  

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